CN104309437B - The method for designing of vehicle air suspension non-linear rigidity real-time optimistic control - Google Patents

Abstract

The present invention relates to the method for designing of vehicle air suspension non-linear rigidity real-time optimistic control, belong to vehicle air suspension technical field, it is characterised in that：According to the nonlinear stiffness characteristic of vehicle air spring, and the real-time Optimal damping ratio of suspension under vehicle current running state, by analytical calculation, obtain the real-time Optimal Stiffness value and the relation between height of vehicle air suspension, by controlling the height of air spring, the real-time control to air suspension Optimal Stiffness is realized.Simply and reliably vehicle air suspension non-linear rigidity real-time optimistic control can be designed using the present invention, and design and testing expenses can be reduced, improve vehicle ride performance and riding comfort.

Description

The method for designing of vehicle air suspension non-linear rigidity real-time optimistic control

Technical field

The present invention relates to vehicle air suspension, the particularly design of vehicle air suspension non-linear rigidity real-time optimistic control Method.

Background technology

The core component of air suspension is air spring, and its principle is to realize elastic reaction using the compressibility of gas, So as to improve the ride performance and riding comfort of vehicle.Understood according to institute's inspection information, due to by air spring nonlinear elasticity Property restriction, current home and abroad fails to be given always simple, reliable to vehicle air suspension non-linear rigidity real-time optimistic control Ground method for designing, not it is proposed that realizing the real-time control to air suspension Optimal Stiffness by controlling air spring height.Mostly It is, using the gas to rubber pneumatic bag charge and discharge different pressures, to increase the methods such as auxiliary air reservoir, regulation throttle orifice aperture, it is right to realize The real-time control of air suspension rigidity.With the fast development of Vehicle Industry, current vehicle air suspension non-linear rigidity is real-time The method for designing of optimum control, it is impossible to meet the design requirement of vehicle development and riding comfort.Therefore, it is necessary to set up a kind of letter Single, reliably vehicle air suspension non-linear rigidity real-time optimistic control method for designing, i.e., according to the non-of vehicle air spring The real-time Optimal damping ratio of suspension under linear rigidity characteristic, and vehicle current running state, by analytical calculation, obtains vehicle empty The real-time Optimal Stiffness value of gas suspension and the relation between height, by controlling the height of air spring, realize outstanding to air The real-time control of frame Optimal Stiffness, further improves vehicle ride performance and riding comfort.

The content of the invention

For defect present in above-mentioned prior art, technical problem solved by the invention be to provide it is a kind of simple, can By the method for designing of ground vehicle air suspension non-linear rigidity real-time optimistic control.

In order to solve the above-mentioned technical problem, vehicle air suspension non-linear rigidity real-time optimistic control provided by the present invention Method for designing, its design cycle block diagram as shown in figure 1, its technical scheme implement comprise the following steps that：

(1) identification of air spring nonlinear stiffness characteristic parameter：

A：Using vibration test equipment, the vehicle single-wheel air suspension peace under certain given travel operating mode is measured and collected The vehicle bridge vertical vibration acceleration signal and bouncing of automobile body acceleration signal of holding position center, collection vibration signal when Between length be { 0, T }={ [0, t₁]+[t₁, T] }, wherein, previous time period [0, t₁] vibration signal be used for air spring non-thread The identification of property stiffness characteristics parameter, latter time period [t₁, T] vibration signal be used for nonlinear stiffness characteristic parameter identification knot The simulating, verifying of fruit；

B：According to the nonlinear stiffness characteristic of air spring, an odd power multinomial F is built_s=k_s1z+k_s3z³, wherein, F_sIt is with the nonlinear elasticity power of the air spring represented by odd power multinomial, k_s1And k_s3It is polynomial parameter to be identified；

C：According to the sprung mass m of vehicle single-wheel air suspension₂, air spring nonlinear stiffness characteristic parameter to be identified k_s1, k_s3, shock absorber damping C_d, build the vehicle vibration model of single-degree-of-freedom 1/4；

D：According to air spring nonlinear elasticity power odd power multinomial constructed in step B, and in step C it is constructed The vehicle vibration model of single-degree-of-freedom 1/4, using Matlab/Simulink simulation softwares, set up vehicle non-linear vibrating system Simulation model, with previous time period [0, t₁] measured by vehicle bridge vertical vibration acceleration signal be input signal, to vehicle body Vertical vibration root mean square of weighed acceleration emulated, wherein, weighted value at different frequencies is：

E：With the nonlinear stiffness characteristic parameter k of air spring_s1, k_s3As identification variable, using [0, t₁] time period Bouncing of automobile body root mean square of weighed acceleration obtained by emulationAdd with the bouncing of automobile body measured by experiment Power acceleration root-mean-square valueSet up the object function J of air spring non-linear rigidity identification_min, i.e.,：

F：Identification object function according to air spring non-linear rigidity, parameter identification object function is sought using optimized algorithm Minimum value, now corresponding optimized variable be identification obtained by air spring nonlinear stiffness characteristic parameter, i.e., k_s1, k_s3；

G：It is constructed in step C according to air spring nonlinear elasticity power odd power multinomial constructed in step B The vehicle vibration model of single-degree-of-freedom 1/4, and the nonlinear stiffness characteristic parameter k of resulting air spring is recognized in F-step_s1, k_s3, with [t₁, T] and the vehicle bridge vertical vibration acceleration signal measured by the time period is input signal, the vertical vibration to vehicle body adds Power acceleration magnitude carries out simulation calculation, and is compared with measured bouncing of automobile body weighted acceleration value within the time period Compared with the identification result to air spring non-linear rigidity is verified；

(2) vehicle travels real-time Optimal damping ratio ξ₀Determination：

I：The bouncing of automobile body acceleration under vehicle current running state is measured using acceleration transducerUsing height Vehicle body of the air suspension upper extreme point installation site center to ground is vertically high under degree sensor measures vehicle current running state Degree h₂, the vehicle bridge vertical height h of lower extreme point installation site center to ground₁；Vehicle current driving is measured using velocity sensor Travel speed v under state；

II：Natural height h according to vehicle air spring₀, and identified vehicle body vertical height h in I steps₂, vehicle bridge hang down Straight height h₁, determine the relative displacement of vehicle current running state under body vertical vibration and analysis of wheel vertical vibration, i.e. z=| h₂- h₁-h₀|；

III：According to the air spring nonlinear stiffness characteristic parameter k obtained by being recognized in step (1)_s1, k_s3, and II steps Identified bouncing of automobile body and the relative displacement z of analysis of wheel vertical vibration, determine the sky under vehicle current motion state in rapid Gas suspension rate K₂, i.e.,：

K₂=k_s1+3k_s3z²；

IV：According to the sprung mass m of vehicle single-wheel air suspension₂, shock absorber damping C_d, shock absorber setting angle α, Identified K in lever ratio i, and III steps₂, determine Current vehicle airsuspension system damping ratio ξ, i.e.,：

V：According to the sprung mass m of vehicle single-wheel air suspension₂, unsprung mass m₁, tire stiffness K_t, determined in I steps Bouncing of automobile body accelerationSky in Vehicle Speed v, III step under identified vehicle current motion state Gas suspension rate K₂, and identified Current vehicle airsuspension system damping ratio ξ in IV steps, determine vehicle current driving road Face power spectral density G_q(n₀), i.e.,：

In formula,n₀=0.1m^-1, it is reference frequency；

VI：According to identified vehicle running surface power spectral density G in V steps_q(n₀), using vehicle in different travelings Speed lower suspension dynamic spring deflection probability distribution and the relation of standard deviation, determine that the suspension under vehicle current motion state moves spacing Stroke [f_dx], i.e.,：

VII：According to the sprung mass m of vehicle single-wheel air suspension₂, unsprung mass m₁, tire stiffness K_t, institute is true in I steps Air suspension stiffness K under the vehicle current motion state determined in fixed vehicle current driving speed v, III step₂, V steps The vehicle running surface power spectral density G of middle determination_q(n₀), and the dynamic stroke-limit [f of identified suspension in VI steps_dx], really Determine vehicle and travel real-time Optimal damping ratio ξ₀, i.e.,：

In formula,n₀=0.1m^-1, it is reference frequency；

(3) under vehicle current running state the real-time Optimal Stiffness K of air suspension determination：

According to the sprung mass m of vehicle single-wheel air suspension₂, shock absorber damping C_d, shock absorber setting angle α, lever Real-time Optimal damping ratio ξ is travelled than identified vehicle in i, and step (2)₀, air hangs under determining vehicle current running state The real-time Optimal Stiffness K of frame, i.e.,：

(4) design of the real-time optimal height controlled quentity controlled variable of air suspension non-linear rigidity：

According to the air spring nonlinear stiffness characteristic parameter k obtained by being recognized in step (1)_s1And k_s3, and step (3) In vehicle air suspension under identified current running state real-time Optimal Stiffness K, to the real-time optimal height of air spring Degree controlled quentity controlled variable Δ h is designed, i.e.,：

The present invention has the advantage that than prior art：

Fail to be given always simply and reliably to design previously for vehicle air suspension non-linear rigidity real-time optimistic control Method, not it is proposed that realizing the real-time control to air suspension Optimal Stiffness by controlling air spring height.Mostly it is to utilize To the gas of rubber pneumatic bag charge and discharge different pressures, increase the methods such as auxiliary air reservoir, regulation throttle orifice aperture, realize outstanding to air The real-time control of frame rigidity, it is impossible to meet the design requirement of vehicle development and vehicle riding comfort.Vehicle air of the present invention hangs The method for designing of frame non-linear rigidity real-time optimistic control, i.e., according to the nonlinear stiffness characteristic of vehicle air spring, and vehicle The real-time Optimal damping ratio of suspension under current running state, by analytical calculation, obtains the real-time optimal firm of vehicle air suspension Angle value and the relation between height, by controlling the height of air spring, realize the real-time control to air suspension Optimal Stiffness System, while experiment and design cost can be reduced, improves vehicle ride performance and riding comfort.

Brief description of the drawings

It is described further below in conjunction with the accompanying drawings for a better understanding of the present invention.

Fig. 1 is the design cycle block diagram of vehicle air spring non-linear rigidity real-time optimistic control；

Fig. 2 is that the vehicle single-wheel air suspension that embodiment experiment is measured accelerates in the vehicle bridge vertical vibration of installation site center Degree signal；

Fig. 3 is that the vehicle single-wheel air suspension that embodiment experiment is measured accelerates in installation site center bouncing of automobile body Degree signal；

Fig. 4 is the vehicle vibration model of embodiment single-degree-of-freedom 1/4；

Fig. 5 is the Simulink simulation models of embodiment vehicle non-linear vibrating system；

Fig. 6 is embodiment sensor mounting location schematic diagram；

Fig. 7 is relation curve of the embodiment air suspension non-linear rigidity with air spring height variable quantity；

Fig. 8 is change curve of the embodiment air spring height variable quantity with speed；

Fig. 9 is change curve of the embodiment air spring height variable quantity with road conditions.

Specific embodiment

The present invention is described in further detail below by an embodiment.

Embodiment：The sprung mass m of certain vehicle single-wheel air suspension₂=400kg, unsprung mass m₁=40kg, air spring Natural height h₀=0.24m, shock absorber damping C_d=2723N.s/m, shock absorber setting angle α=10 °, lever ratio i= 0.9, tire stiffness K_t=260000N/m, the vehicle is travelled with 80km/h speed on a highway.To the vehicle air suspension The real-time optimal height controlled quentity controlled variable of non-linear rigidity is designed.

The method for designing of the vehicle air suspension non-linear rigidity real-time optimistic control that the embodiment of the present invention is provided, specifically Step is as follows：

(1) identification of air spring non-linear rigidity：

A：Using vibration test equipment, the vehicle is measured and collected when highway is travelled with 80km/h speed, Vehicle bridge vertical vibration acceleration signal and bouncing of automobile body the acceleration letter of vehicle single-wheel air suspension installation site center Number, respectively as shown in Figures 2 and 3, the time span for gathering vibration signal is 120s, wherein, previous time period [0,60s] shakes Dynamic signal is used for the identification of air spring non-linear rigidity, and the vibration signal of latter time period [60s, 120s] is used for non-linear The simulating, verifying of rigidity identification result；

B：According to the nonlinear stiffness characteristic of air spring, an odd power multinomial F is built_s=k_s1z+k_s3z³, wherein, F_sIt is with the nonlinear elasticity power of the air spring represented by odd power multinomial, k_s1And k_s3It is polynomial parameter to be identified；

C：According to the sprung mass m of vehicle single-wheel air suspension₂=400kg, air spring non-linear rigidity to be identified Characterisitic parameter k_s1, k_s3, shock absorber damping C_d=2723N.s/m, builds the vehicle vibration model of single-degree-of-freedom 1/4, such as Fig. 4 institutes Show；

D：According to air spring nonlinear elasticity power odd power multinomial constructed in step B, and in step C it is constructed The vehicle vibration model of single-degree-of-freedom 1/4, using Matlab/Simulink simulation softwares, set up vehicle non-linear vibrating system Simulation model, as shown in figure 5, being input with the vehicle bridge vertical vibration acceleration signal measured by previous time period [0,60s] Signal, the vertical vibration root mean square of weighed acceleration to vehicle body is emulated, wherein, weighted value at different frequencies is：

E：With the nonlinear stiffness characteristic parameter k of air spring_s1, k_s3As identification variable, using in [0, the 60s] time Bouncing of automobile body root mean square of weighed acceleration obtained by section emulationWith the bouncing of automobile body measured by experiment Root mean square of weighed accelerationSet up the object function J of air spring non-linear rigidity identification_min, i.e.,：

F：Identification object function according to air spring non-linear rigidity, parameter identification object function is sought using optimized algorithm Minimum value, now corresponding optimized variable be identification obtained by air spring nonlinear stiffness characteristic parameter, i.e., k_s1=495.2N/m, k_s3=6.08 × 10⁶N/m³；

G：It is constructed in step C according to air spring nonlinear elasticity power odd power multinomial constructed in step B The vehicle vibration model of single-degree-of-freedom 1/4, and the nonlinear stiffness characteristic parameter k of resulting air spring is recognized in F-step_s1= 495.2N/m, k_s3=6.08 × 10⁶N/m³, it is with the vehicle bridge vertical vibration acceleration signal measured by [60s, the 120s] time period Input signal, carries out simulation calculation to the vertical vibration weighted acceleration value of vehicle body, and with measured car within the time period Body vertical vibration weighted acceleration value is compared, and the identification result to air spring non-linear rigidity is verified, wherein, The simulation value of the body vibrations weighted acceleration in latter time period [60s, 120s] is 0.416m/s², experimental test value is 0.419m/s², both deviations are only 0.003m/s², show that the discrimination method of the air spring non-linear rigidity set up is correct 's；

(2) vehicle travels real-time Optimal damping ratio ξ₀Determination：

I：The bouncing of automobile body acceleration under vehicle current running state is measured using acceleration transducerAir suspension upper extreme point installation site center under vehicle current running state is measured using height sensor To the vehicle body vertical height h on ground₂=0.59m, the vehicle bridge vertical height h of lower extreme point installation site center to ground₁= 0.31m；The travel speed v=80km/h under vehicle current running state is measured using velocity sensor；Wherein, the peace of sensor Holding position schematic diagram is as shown in Figure 6；

II：Natural height h according to vehicle air spring₀Identified vehicle body vertical height h in=0.24m, and I steps₂ =0.59m, vehicle bridge vertical height h₁=0.31m, determines that vehicle current running state under body vertical vibration is shaken with analysis of wheel vertical Dynamic relative displacement, i.e. z=| h₂-h₁-h₀|=0.04m；

III：According to the air spring nonlinear stiffness characteristic parameter k obtained by being recognized in step (1)_s1=495.2N/m, k_s3=6.08 × 10⁶N/m³, and the relative displacement z=that identified bouncing of automobile body vibrates with analysis of wheel vertical in II steps 0.04m, determines the air suspension stiffness K under vehicle current motion state₂, i.e.,：

K₂=K_s1+3K_s3z²=29679N/m；

IV：According to the sprung mass m of vehicle single-wheel air suspension₂=400kg, shock absorber damping C_d=2723N.s/ M, shock absorber setting angle α=10 °, identified K in lever ratio i=0.9, and III steps₂=29679N/m, it is determined that currently Vehicle air suspension system damping ratio ξ, i.e.,：

V：According to the sprung mass m of vehicle single-wheel air suspension₂=400kg, unsprung mass m₁=40kg, tire stiffness K_t Identified bouncing of automobile body acceleration in=260000N/m, I stepVehicle Speed v= Air suspension stiffness K in 80km/h, III step under identified vehicle current motion state₂=29679N/m, and IV steps In identified Current vehicle airsuspension system damping ratio ξ=0.31, determine vehicle current driving Road Surface Power Spectrum Density G_q (n₀), i.e.,：

In formula,n₀=0.1m^-1, it is to refer to space Frequency；

VI：According to identified vehicle running surface power spectral density G in V steps_q(n₀)=3.33 × 10^-5m³, using car Different travel speed lower suspension dynamic spring deflection probability distribution and standard deviation relation, under determining vehicle current motion state The dynamic stroke-limit [f of suspension_dx], i.e.,：[f_dx]=0.05m；

VII：According to the sprung mass m of vehicle single-wheel air suspension₂=400kg, unsprung mass m₁=40kg, tire stiffness

K_tDetermine in identified vehicle current driving speed v=80km/h, III step in=260000N/m, I step Vehicle current motion state under air suspension stiffness K₂The vehicle running surface power determined in=29679N/m, V step Spectrum density

G_q(n₀)=3.33 × 10^-5m³, and the dynamic stroke-limit [f of identified suspension in VI steps_dx]=0.05m, it is determined that Vehicle travels real-time Optimal damping ratio ξ₀, i.e.,：ξ₀=0.18；

(3) under vehicle current running state the real-time Optimal Stiffness K of air suspension determination：

According to the sprung mass m of vehicle single-wheel air suspension₂=400kg, shock absorber damping C_d=2723N.s/m, subtracts Shake device setting angle α=10 °, and identified vehicle travels real-time Optimal damping ratio ξ in lever ratio i=0.9, and step (2)₀= 0.18, determine the real-time Optimal Stiffness K of air suspension under vehicle current running state, i.e.,：

(4) design of the real-time optimal height controlled quentity controlled variable of air suspension non-linear rigidity：

According to the air spring nonlinear stiffness characteristic parameter k obtained by being recognized in step (1)_s1=495.2N/m, k_s3= 6.08×10⁶N/m³, and the vehicle air suspension in step (3) under identified current running state real-time Optimal Stiffness K= 88269N/m, the real-time optimal height controlled quentity controlled variable Δ h to air spring is designed, i.e.,：

Wherein, the vehicle air suspension non-linear rigidity with air spring height variable quantity relation curve as shown in fig. 7, Air spring height variable quantity is with the change curve of speed as shown in figure 8, air spring height variable quantity is bent with the change of road conditions Line is as shown in Figure 9.

Claims (1)

1. the method for designing of vehicle air suspension non-linear rigidity real-time optimistic control, its specific design step is as follows：

(1) identification of air spring nonlinear stiffness characteristic parameter：

A：Using vibration test equipment, the vehicle single-wheel air suspension installation position under certain given travel operating mode is measured and collected The vehicle bridge vertical vibration acceleration signal and bouncing of automobile body acceleration signal of center are put, the time for gathering vibration signal is long It is { 0, T }={ [0, t to spend₁]+[t₁, T] }, wherein, previous time period [0, t₁] vibration signal be used for air spring it is non-linear just Spend the identification of characterisitic parameter, latter time period [t₁, T] vibration signal be used for nonlinear stiffness characteristic parameter identification result Simulating, verifying；

B：According to the nonlinear stiffness characteristic of air spring, an odd power multinomial F is built_s=k_s1z+k_s3z³, wherein, F_sFor With the nonlinear elasticity power of the air spring represented by odd power multinomial, k_s1And k_s3It is polynomial parameter to be identified；

C：According to the sprung mass m of vehicle single-wheel air suspension₂, air spring nonlinear stiffness characteristic parameter k to be identified_s1, k_s3, shock absorber damping C_d, build the vehicle vibration model of single-degree-of-freedom 1/4；

D：According to air spring nonlinear elasticity power odd power multinomial constructed in step B, and list constructed in step C The vehicle vibration model of the free degree 1/4, using Matlab/Simulink simulation softwares, sets up the emulation of vehicle non-linear vibrating system Model, with previous time period [0, t₁] measured by vehicle bridge vertical vibration acceleration signal be input signal, vehicle body is hung down Straight vibration root mean square of weighed acceleration is emulated, wherein, weighted value at different frequencies is：

$w_k\left(f_i\right)=\left\{\begin{array}{cc}0.5,& f_i\∈\[0.5,2\]Hz\\ f_i/4,& f_i\∈(2,4\]Hz\\ 1,& f_i\∈(4,12.5\]Hz\\ 12.5/f_i,& f_i\∈(12.5,80\]Hz\end{array}\right.;$

E：With the nonlinear stiffness characteristic parameter k of air spring_s1, k_s3As identification variable, using [0, t₁] time period emulation Resulting bouncing of automobile body root mean square of weighed accelerationAdd with the bouncing of automobile body weighting measured by experiment Speed root-mean-square valueSet up the object function J of air spring non-linear rigidity identification_min, i.e.,：

$J_{\min }={({\mathrm{\σ}}_{{\stackrel{\·\·}{z}}_s\_sim}-{\mathrm{\σ}}_{{\stackrel{\·\·}{z}}_s\_test})}^2;$

F：Identification object function according to air spring non-linear rigidity, parameter identification object function is sought most using optimized algorithm Small value, now corresponding optimized variable is the nonlinear stiffness characteristic parameter of the air spring obtained by identification, i.e. k_s1, k_s3；

G：According to air spring nonlinear elasticity power odd power multinomial constructed in step B, in step C it is constructed it is single from By spending 1/4 vehicle vibration model, and the nonlinear stiffness characteristic parameter k that resulting air spring is recognized in F-step_s1, k_s3, With [t₁, T] the vehicle bridge vertical vibration acceleration signal measured by the time period is input signal, vertical vibration weighting to vehicle body plus Velocity amplitude carries out simulation calculation, and is compared with measured bouncing of automobile body weighted acceleration value within the time period, Identification result to air spring non-linear rigidity is verified；

(2) vehicle travels real-time Optimal damping ratio ξ₀Determination：

I：The bouncing of automobile body acceleration under vehicle current running state is measured using acceleration transducerPassed using height Sensor measures vehicle body vertical height h of the air suspension upper extreme point installation site center to ground under vehicle current running state₂, Vehicle bridge vertical height h of the lower extreme point installation site center to ground₁；Vehicle current running state is measured using velocity sensor Under travel speed v；

II：Natural height h according to vehicle air spring₀, and identified vehicle body vertical height h in I steps₂, vehicle bridge is vertically high Degree h₁, determine the relative displacement of vehicle current running state under body vertical vibration and analysis of wheel vertical vibration, i.e. z=| h₂-h₁-h₀ |；

III：According to the air spring nonlinear stiffness characteristic parameter k obtained by being recognized in step (1)_s1, k_s3, and institute in II steps The bouncing of automobile body of determination and the relative displacement z of analysis of wheel vertical vibration, determine the air suspension under vehicle current motion state Stiffness K₂, i.e.,：

K₂=k_s1+3k_s3z²；

IV：According to the sprung mass m of vehicle single-wheel air suspension₂, shock absorber damping C_d, shock absorber setting angle α, lever Than identified K in i, and III steps₂, determine Current vehicle airsuspension system damping ratio ξ, i.e.,：

$\mathrm{\ξ}=\frac{C_d{i}^2{\cos }^2\mathrm{\α}}{2\sqrt{K_2{m}_2}};$

V：According to the sprung mass m of vehicle single-wheel air suspension₂, unsprung mass m₁, tire stiffness K_t, identified car in I steps Body vertical vibration accelerationAir in Vehicle Speed v, III step under identified vehicle current motion state hangs Frame stiffness K₂, and identified Current vehicle airsuspension system damping ratio ξ in IV steps, determine vehicle current driving road surface work( Rate spectrum density G_q(n₀), i.e.,：

$G_q\left(n_0\right)=\frac{{\mathrm{\ξr}}_m{{\stackrel{\·\·}{z}}_2}^2}{4{\mathrm{\π}}^5{f}_0^3{n}_0^{2}v(1+r_m+4r_m{r}_k{\mathrm{\ξ}}^2)};$

In formula,N0=0.1m-¹, it is reference frequency；

VI：According to identified vehicle running surface power spectral density G in V steps_q(n₀), using vehicle in different travel speeds Lower suspension dynamic spring deflection probability distribution and the relation of standard deviation, determine the dynamic stroke-limit of suspension under vehicle current motion state [f_dx], i.e.,：

$\&lsqb;f_{dx}\&rsqb;=\left\{\begin{array}{cc}0.03,& 0\&le;G_q\left(n_0\right)\&le;32\&times;{10}^{-6}\\ 0.05,& 32\&times;{10}^{-6}<G_q\left(n_0\right)\&le;128\&times;{10}^{-6}\\ 0.07,& 128\&times;{10}^{-6}<G_q\left(n_0\right)\&le;512\&times;{10}^{-6}\\ 0.09,& 512\&times;{10}^{-6}<G_q\left(n_0\right)\&le;2048\&times;{10}^{-6}\\ 0.135,& G_q\left(n_0\right)>2048\&times;{10}^{-6}\end{array}\right.;$

VII：According to the sprung mass m of vehicle single-wheel air suspension₂, unsprung mass m₁, tire stiffness K_t, it is identified in I steps Air suspension stiffness K under the vehicle current motion state determined in vehicle current driving speed v, III step₂, in V steps really Fixed vehicle running surface power spectral density G_q(n₀), and the dynamic stroke-limit [f of identified suspension in VI steps_dx], determine car The real-time Optimal damping ratio ξ of traveling₀, i.e.,：

${\mathrm{\&xi;}}_0=\left\{\begin{array}{cc}\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}},& 9{\mathrm{\&pi;G}}_q\left(n_0\right)n_0^{2}v\frac{1+r_m}{4f_0{r}_m{\&lsqb;f_{dx}\&rsqb;}^2}\&le;\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}}\\ 9{\mathrm{\&pi;G}}_q\left(n_0\right)n_0^{2}v\frac{1+r_m}{4f_0{r}_m{\&lsqb;f_{dx}\&rsqb;}^2},& \frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}}<9{\mathrm{\&pi;G}}_q\left(n_0\right)n_0^{2}v\frac{1+r_m}{4f_0{r}_m{\&lsqb;f_{dx}\&rsqb;}^2}\&le;\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}+\frac{r_m{r}_k-2-2r_m}{{(1+r_m)}^2}}\\ \frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}+\frac{r_m{r}_k-2-2r_m}{{(1+r_m)}^2}},& 9{\mathrm{\&pi;G}}_q\left(n_0\right)n_0^{2}v\frac{1+r_m}{4f_0{r}_m{\&lsqb;f_{dx}\&rsqb;}^2}\&GreaterEqual;\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}+\frac{r_m{r}_k-2-2r_m}{{(1+r_m)}^2}}\end{array}\right.;$

In formula,n₀=0.1m^-1, it is reference frequency；

(3) under vehicle current running state the real-time Optimal Stiffness K of air suspension determination：

According to the sprung mass m of vehicle single-wheel air suspension₂, shock absorber damping C_d, shock absorber setting angle α, lever ratio i, And identified vehicle travels real-time Optimal damping ratio ξ in step (2)₀, determine air suspension under vehicle current running state Real-time Optimal Stiffness K, i.e.,：

$K=\frac{{C_d}^2{i}^4{\cos }^4\mathrm{\&alpha;}}{4{\mathrm{\&xi;}}_0^2{m}_2};$

(4) design of the real-time optimal height controlled quentity controlled variable of air suspension non-linear rigidity：

According to the air spring nonlinear stiffness characteristic parameter k obtained by being recognized in step (1)_s1And k_s3, and the middle institute of step (3) is really The real-time Optimal Stiffness K of the vehicle air suspension under fixed current running state, the real-time optimal height control to air spring Amount Δ h is designed, i.e.,：

$\mathrm{\&Delta;}h=\sqrt{\frac{K-k_{s1}}{3k_{s3}}}.$